Precalculus Examples

x2-(3-y)2=24x2(3y)2=24
Step 1
Simplify the left side x2-(3-y)2x2(3y)2.
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Step 1.1
Simplify each term.
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Step 1.1.1
Rewrite (3-y)2(3y)2 as (3-y)(3-y)(3y)(3y).
x2-((3-y)(3-y))=24x2((3y)(3y))=24
Step 1.1.2
Expand (3-y)(3-y)(3y)(3y) using the FOIL Method.
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Step 1.1.2.1
Apply the distributive property.
x2-(3(3-y)-y(3-y))=24x2(3(3y)y(3y))=24
Step 1.1.2.2
Apply the distributive property.
x2-(33+3(-y)-y(3-y))=24x2(33+3(y)y(3y))=24
Step 1.1.2.3
Apply the distributive property.
x2-(33+3(-y)-y3-y(-y))=24x2(33+3(y)y3y(y))=24
x2-(33+3(-y)-y3-y(-y))=24x2(33+3(y)y3y(y))=24
Step 1.1.3
Simplify and combine like terms.
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Step 1.1.3.1
Simplify each term.
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Step 1.1.3.1.1
Multiply 33 by 33.
x2-(9+3(-y)-y3-y(-y))=24x2(9+3(y)y3y(y))=24
Step 1.1.3.1.2
Multiply -11 by 33.
x2-(9-3y-y3-y(-y))=24x2(93yy3y(y))=24
Step 1.1.3.1.3
Multiply 33 by -11.
x2-(9-3y-3y-y(-y))=24x2(93y3yy(y))=24
Step 1.1.3.1.4
Rewrite using the commutative property of multiplication.
x2-(9-3y-3y-1(-1yy))=24x2(93y3y1(1yy))=24
Step 1.1.3.1.5
Multiply yy by yy by adding the exponents.
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Step 1.1.3.1.5.1
Move yy.
x2-(9-3y-3y-1(-1(yy)))=24x2(93y3y1(1(yy)))=24
Step 1.1.3.1.5.2
Multiply yy by yy.
x2-(9-3y-3y-1(-1y2))=24x2(93y3y1(1y2))=24
x2-(9-3y-3y-1(-1y2))=24x2(93y3y1(1y2))=24
Step 1.1.3.1.6
Multiply -11 by -11.
x2-(9-3y-3y+1y2)=24x2(93y3y+1y2)=24
Step 1.1.3.1.7
Multiply y2y2 by 11.
x2-(9-3y-3y+y2)=24x2(93y3y+y2)=24
x2-(9-3y-3y+y2)=24x2(93y3y+y2)=24
Step 1.1.3.2
Subtract 3y3y from -3y3y.
x2-(9-6y+y2)=24x2(96y+y2)=24
x2-(9-6y+y2)=24x2(96y+y2)=24
Step 1.1.4
Apply the distributive property.
x2-19-(-6y)-y2=24x219(6y)y2=24
Step 1.1.5
Simplify.
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Step 1.1.5.1
Multiply -11 by 99.
x2-9-(-6y)-y2=24x29(6y)y2=24
Step 1.1.5.2
Multiply -66 by -11.
x2-9+6y-y2=24x29+6yy2=24
x2-9+6y-y2=24x29+6yy2=24
x2-9+6y-y2=24x29+6yy2=24
Step 1.2
Reorder.
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Step 1.2.1
Move -99.
x2+6y-y2-9=24x2+6yy29=24
Step 1.2.2
Move 6y6y.
x2-y2+6y-9=24x2y2+6y9=24
x2-y2+6y-9=24x2y2+6y9=24
x2-y2+6y-9=24x2y2+6y9=24
Step 2
Set the equation equal to zero.
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Step 2.1
Subtract 2424 from both sides of the equation.
x2-y2+6y-9-24=0x2y2+6y924=0
Step 2.2
Subtract 2424 from -99.
x2-y2+6y-33=0x2y2+6y33=0
x2-y2+6y-33=0x2y2+6y33=0
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